In the context of inverse problems, a mathematical model of the measurements is called the direct problem. To understand this term, let us consider a model for obstetric sonography. An ultrasonic ...

Inverse problems in differential equations constitute a pivotal area in applied mathematics and engineering, where the aim is to deduce unknown parameters or inputs within a differential equation from ...

Check back in Fall 2025. Abstract: Constitutive or material models provide a mathematical description of how solids respond to mechanical stimuli. For example, an isotropic linear elastic constitutive ...

Cauchy problems and inverse problems in partial differential equations (PDEs) represent a class of challenging mathematical models where one seeks to determine unknown data inside a domain from ...